We give a concrete description of the category of étale algebras over the ring of Witt vectors of a given finite length with entries in an arbitrary ring. We do this not only for the classical… (More)

This is an account of the étale topology of generalized Witt vectors. Its purpose is to develop some foundational material needed in Λalgebraic geometry. The theory of the usual, “p-typical” Witt… (More)

Let A be a complete discrete valuation ring with possibly imperfect residue field. The purpose of this paper is to give a notion of conductor for Galois representations over A that generalizes the… (More)

This is an account of the algebraic geometry of Witt vectors and arithmetic jet spaces. The usual, “p-typical” Witt vectors of p-adic schemes of finite type are already reasonably well understood.… (More)

The notion of aZ-algebra has a non-linear analogue, whose purpose it is to control operations on commutative rings rather than linear operations on abelian groups. These plethoriescan also be… (More)

We show that any Λ-ring, in the sense of Riemann–Roch theory, which is finite étale over the rational numbers and has an integral model as a Λ-ring is contained in a product of cyclotomic fields. In… (More)

We study derivations and differential forms on the arithmetic jet spaces of smooth schemes, relative to several primes. As applications we give a new interpretation of arithmetic Laplacians and we… (More)

The theory of Λ-rings, in the sense of Grothendieck’s Riemann– Roch theory, is an enrichment of the theory of commutative rings. In the same way, we can enrich usual algebraic geometry over the ring… (More)

Let A be a complete discrete valuation ring with possibly imperfect residue field, and let χ be a one-dimensional Galois representation over A. I show that the non-logarithmic variant of Kato's Swan… (More)

Cellular and wireline (WiFi VoIP & VoIP over wired broad band) convergence is being driven by the value a unified wireline/wireless service brings to the end-user (consumer, enterprise) and operator.… (More)